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Sid Singh Sane
Asked: 2022-11-07T05:41:14+05:30 In:

Let the random variable X is defined as time (in minutes) that elapses between the bell and end of the lecture in case of collagen professor whrer pdf is defined as `f(x)={{:(kx^2″,”0lexlt2),(0″, “”elsewhere”):}`
find the probability that lecture continue for atleast 90s beyond the bell
A. `(37)/(64)`
B. `(35)/(64)`
C. `(33)/(69)`
D. None of these

Let the random variable X is defined as time (in minutes) that elapses between the bell and end of the lecture in case of collagen professor whrer pdf is defined as `f(x)={{:(kx^2″,”0lexlt2),(0″, “”elsewhere”):}`
find the probability that lecture continue for atleast 90s beyond the bell
A. `(37)/(64)`
B. `(35)/(64)`
C. `(33)/(69)`
D. None of these
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  1. Correct Answer – A
    We known that `oversetoounderset(-oo)intf(x)dx=1`
    `therefore” “0+underset0overset2intf(x)dx=1`
    `rArr” “underset0overset2intkx^2dx=1`
    `rArr” “k[x^3/3]_0^2=1rArr[8/3]=1`
    `rArr” “k=3/8`
    Clearly, the probability that the lecture continuous for at least 90s i.e.`3/2` min beyond the bell
    `=P(3/2lexle2)=overset2underset(3//2)intf(x)dx=k””overset2underset(3//2)intx^2dx`
    `=k[x^3/3]_(3//2)^2=k/3[8-(27)/8]=(37k)/(24)`
    `=(37xx3/8)/(24)=(37)/(64)`

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